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Let D E be an extension of integral domains, 0 a numerical semigroup with 0 ( N0, 0 D 0nf0g and RD DC ET0 U. In this paper, we completely characterize when R is a weakly Krull domain, an AWFD or a GWFD. We also prove that R is never a WFD. Let T.D/ be the abelian group of t-invertible fractional t-ideals of D under the t- multiplication I JD.I J/t , and let Inv.D/ and Prin.D/ be the subgroups of T.D/ consisting respectively of invertible fractional ideals of D and nonzero principal fractional ideals of D. Then it is clear that Prin.D/ Inv.D/ T.D/. The t-class group of D is an abelian group Cl.D/D T.D/= Prin.D/ and the Picard group Pic.D/D Inv.D/= Prin.D/ is a subgroup of Cl.D/. The local t-class group G.D/ of D is defined by G.D/D Cl.D/= Pic.D/. Let X 1 .D/ stand for the set of height-one prime ideals of D. We say that D is a weakly Krull domain if DD T P2X 1 .D/ DP and this intersection has finite character, i.e., each nonzero element d2 D is a unit in DP for all but a finite number of P's in X 1 .D/; D is a weakly factorial domain (WFD) if every nonzero nonunit element of D is a product of primary elements; D is an almost weakly factorial domain

Weakly Krull domains and the composite numerical semigroup ringD+E[Γ∗]

Weakly Krull domains and the composite numerical semigroup ringD+E[Γ^∗]